{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 代表的な連続型確率分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.564080Z",
     "start_time": "2018-08-11T14:40:49.294680Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats, integrate\n",
    "from scipy.optimize import minimize_scalar\n",
    "\n",
    "%precision 3\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.605993Z",
     "start_time": "2018-08-11T14:40:49.565532Z"
    }
   },
   "outputs": [],
   "source": [
    "linestyles = ['-', '--', ':']\n",
    "\n",
    "def E(X, g=lambda x: x):\n",
    "    x_range, f = X\n",
    "    def integrand(x):\n",
    "        return g(x) * f(x)\n",
    "    return integrate.quad(integrand, -np.inf, np.inf)[0]\n",
    "\n",
    "def V(X, g=lambda x: x):\n",
    "    x_range, f = X\n",
    "    mean = E(X, g)\n",
    "    def integrand(x):\n",
    "        return (g(x) - mean) ** 2 * f(x)\n",
    "    return integrate.quad(integrand, -np.inf, np.inf)[0]\n",
    "\n",
    "def check_prob(X):\n",
    "    x_range, f = X\n",
    "    f_min = minimize_scalar(f).fun\n",
    "    assert f_min >= 0, '密度関数が負の値をとります'\n",
    "    prob_sum = np.round(integrate.quad(f, -np.inf, np.inf)[0], 6)\n",
    "    assert prob_sum == 1, f'確率の和が{prob_sum}になりました'\n",
    "    print(f'期待値は{E(X):.3f}')\n",
    "    print(f'分散は{V(X):.3f}')\n",
    "    \n",
    "def plot_prob(X, x_min, x_max):\n",
    "    x_range, f = X\n",
    "    def F(x):\n",
    "        return integrate.quad(f, -np.inf, x)[0]\n",
    "\n",
    "    xs = np.linspace(x_min, x_max, 100)\n",
    "\n",
    "    fig = plt.figure(figsize=(10, 6))\n",
    "    ax = fig.add_subplot(111)\n",
    "    ax.plot(xs, [f(x) for x in xs],\n",
    "            label='f(x)', color='gray')\n",
    "    ax.plot(xs, [F(x) for x in xs],\n",
    "            label='F(x)', ls='--', color='gray')\n",
    "\n",
    "    ax.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 正規分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.611086Z",
     "start_time": "2018-08-11T14:40:49.607370Z"
    }
   },
   "outputs": [],
   "source": [
    "def N(mu, sigma):\n",
    "    x_range = [- np.inf, np.inf]\n",
    "    def f(x):\n",
    "        return 1 / np.sqrt(2 * np.pi * sigma**2) *\\\n",
    "                    np.exp(-(x-mu)**2 / (2 * sigma**2))\n",
    "    return x_range, f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.615097Z",
     "start_time": "2018-08-11T14:40:49.612596Z"
    }
   },
   "outputs": [],
   "source": [
    "mu, sigma = 2, 0.5\n",
    "X = N(mu, sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.623516Z",
     "start_time": "2018-08-11T14:40:49.616477Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "期待値は2.000\n",
      "分散は0.250\n"
     ]
    }
   ],
   "source": [
    "check_prob(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.733482Z",
     "start_time": "2018-08-11T14:40:49.624900Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_prob(X, 0, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.737689Z",
     "start_time": "2018-08-11T14:40:49.735056Z"
    }
   },
   "outputs": [],
   "source": [
    "rv = stats.norm(2, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.741973Z",
     "start_time": "2018-08-11T14:40:49.738668Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.0, 0.25)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv.mean(), rv.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.745679Z",
     "start_time": "2018-08-11T14:40:49.742957Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7978845608028654"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv.pdf(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.749453Z",
     "start_time": "2018-08-11T14:40:49.746706Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.27425311775007355"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv.cdf(1.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.753482Z",
     "start_time": "2018-08-11T14:40:49.750532Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2622002563540207"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv.isf(0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.757444Z",
     "start_time": "2018-08-11T14:40:49.754480Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.1775731865242636, 2.822426813475736)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv.interval(0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.761437Z",
     "start_time": "2018-08-11T14:40:49.758414Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.1775731865242638, 2.8224268134757367)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv.isf(0.95), rv.isf(0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.857068Z",
     "start_time": "2018-08-11T14:40:49.762445Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "xs = np.linspace(-5, 5, 100)\n",
    "params = [(0, 1), (0, 2), (1, 1)]\n",
    "for param, ls in zip(params, linestyles):\n",
    "    mu, sigma = param\n",
    "    rv = stats.norm(mu, sigma)\n",
    "    ax.plot(xs, rv.pdf(xs),\n",
    "            label=f'N({mu}, {sigma**2})', ls=ls, color='gray')\n",
    "ax.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 指数分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.861824Z",
     "start_time": "2018-08-11T14:40:49.858099Z"
    }
   },
   "outputs": [],
   "source": [
    "def Ex(lam):\n",
    "    x_range = [0, np.inf]\n",
    "    def f(x):\n",
    "        if x >= 0:\n",
    "            return lam * np.exp(-lam * x)\n",
    "        else:\n",
    "            return 0\n",
    "    return x_range, f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.866436Z",
     "start_time": "2018-08-11T14:40:49.862979Z"
    }
   },
   "outputs": [],
   "source": [
    "lam = 3\n",
    "X = Ex(lam)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.872854Z",
     "start_time": "2018-08-11T14:40:49.867736Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "期待値は0.333\n",
      "分散は0.111\n"
     ]
    }
   ],
   "source": [
    "check_prob(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:49.995738Z",
     "start_time": "2018-08-11T14:40:49.874108Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_prob(X, 0, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:50.107825Z",
     "start_time": "2018-08-11T14:40:49.996898Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "xs = np.linspace(0, 3, 100)\n",
    "for lam, ls in zip([1, 2, 3], linestyles):\n",
    "    rv = stats.expon(scale=1/lam)\n",
    "    ax.plot(xs, rv.pdf(xs),\n",
    "            label=f'lambda:{lam}', ls=ls, color='gray')\n",
    "ax.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## カイ二乗分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:50.513789Z",
     "start_time": "2018-08-11T14:40:50.108877Z"
    }
   },
   "outputs": [],
   "source": [
    "n = 10\n",
    "rv = stats.norm()\n",
    "sample_size = int(1e6)\n",
    "# 標準正規分布から10×100万のサイズで無作為抽出\n",
    "Zs_sample = rv.rvs((n, sample_size))\n",
    "# axis=0の方向で総和をとり、標準正規分布の二乗和の標本データを得る\n",
    "chi2_sample = np.sum(Zs_sample**2, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:42:55.108558Z",
     "start_time": "2018-08-11T14:42:54.924103Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "rv_true = stats.chi2(n)\n",
    "xs = np.linspace(0, 30, 100)\n",
    "ax.hist(chi2_sample, bins=100, density=True,\n",
    "        alpha=0.5, label='chi2_sample')\n",
    "ax.plot(xs, rv_true.pdf(xs), label=f'chi2({n})', color='gray')\n",
    "\n",
    "ax.legend()\n",
    "ax.set_xlim(0, 30)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:50.791097Z",
     "start_time": "2018-08-11T14:40:50.697174Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "xs = np.linspace(0, 20, 500)\n",
    "for n, ls in zip([3, 5, 10], linestyles):\n",
    "    rv = stats.chi2(n)\n",
    "    ax.plot(xs, rv.pdf(xs),\n",
    "            label=f'chi2({n})', ls=ls, color='gray')\n",
    "    \n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:50.796126Z",
     "start_time": "2018-08-11T14:40:50.792418Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11.070497693516355"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv = stats.chi2(5)\n",
    "rv.isf(0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## t分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:50.898734Z",
     "start_time": "2018-08-11T14:40:50.797147Z"
    }
   },
   "outputs": [],
   "source": [
    "n = 10\n",
    "rv1 = stats.norm()\n",
    "rv2 = stats.chi2(n)\n",
    "\n",
    "sample_size = int(1e6)\n",
    "Z_sample = rv1.rvs(sample_size)\n",
    "chi2_sample = rv2.rvs(sample_size)\n",
    "\n",
    "t_sample = Z_sample / np.sqrt(chi2_sample/n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:51.087025Z",
     "start_time": "2018-08-11T14:40:50.899750Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "rv = stats.t(n)\n",
    "xs = np.linspace(-3, 3, 100)\n",
    "ax.hist(t_sample, bins=100, range=(-3, 3),\n",
    "        density=True, alpha=0.5, label='t_sample')\n",
    "ax.plot(xs, rv.pdf(xs), label=f't({n})', color='gray')\n",
    "\n",
    "ax.legend()\n",
    "ax.set_xlim(-3, 3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:51.189656Z",
     "start_time": "2018-08-11T14:40:51.088230Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "xs = np.linspace(-3, 3, 100)\n",
    "for n, ls in zip([3, 5, 10], linestyles):\n",
    "    rv = stats.t(n)\n",
    "    ax.plot(xs, rv.pdf(xs),\n",
    "            label=f't({n})', ls=ls, color='gray')\n",
    "rv = stats.norm()\n",
    "ax.plot(xs, rv.pdf(xs), label='N(0, 1)')\n",
    "    \n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:51.195480Z",
     "start_time": "2018-08-11T14:40:51.190670Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0150483726691575"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv = stats.t(5)\n",
    "rv.isf(0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## F分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:51.315015Z",
     "start_time": "2018-08-11T14:40:51.196762Z"
    }
   },
   "outputs": [],
   "source": [
    "n1 = 5\n",
    "n2 = 10\n",
    "rv1 = stats.chi2(n1)\n",
    "rv2 = stats.chi2(n2)\n",
    "\n",
    "sample_size = int(1e6)\n",
    "sample1 = rv1.rvs(sample_size)\n",
    "sample2 = rv2.rvs(sample_size)\n",
    "\n",
    "f_sample = (sample1/n1) / (sample2/n2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:51.498593Z",
     "start_time": "2018-08-11T14:40:51.316303Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "rv = stats.f(n1, n2)\n",
    "xs = np.linspace(0, 6, 200)[1:]\n",
    "ax.hist(f_sample, bins=100, range=(0, 6),\n",
    "        density=True, alpha=0.5, label='f_sample')\n",
    "ax.plot(xs, rv.pdf(xs), label=f'F({n1}, {n2})', color='gray')\n",
    "\n",
    "ax.legend()\n",
    "ax.set_xlim(0, 6)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T14:40:51.592600Z",
     "start_time": "2018-08-11T14:40:51.499654Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "xs = np.linspace(0, 6, 200)[1:]\n",
    "for n1, ls in zip([3, 5, 10], linestyles):\n",
    "    rv = stats.f(n1, 10)\n",
    "    ax.plot(xs, rv.pdf(xs),\n",
    "            label=f'F({n1}, 10)', ls=ls, color='gray')\n",
    "    \n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  },
  "toc": {
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": "block",
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
